ANSWERS  TO  PROBLEMS 


IN 

LEMEFTS  OF  ELECTRICITY 

FOR 

TECHNICAL  STUDENTS 


BY 

W.  H.  TIMBIE 


NEW  YORK 

JOHN  WILEY  & SONS,  Inc. 

London:  CHAPMAN  & HALL,  Limited 

1916 


Copyright,  1912 

BY 

W.  H.  TIMBIE 


/ 


PRESS  OF 

BRAUNWORTH  & CO. 
BOOK  MANUFACTURERS 
BROOKLYN.  N.  Y. 


PREFACE 


n 


The  following  text  contains  the  answers  to  the  problems  as  they 
appear  in  the  “ First  Edition,  Fourteenth  Thousand,” 

In  publishing  the  answers  to  eight  hundred  problems,  it  is  practi- 
cally impossible  to  put  out  a text  which  shall  be  entirely  free  from  errors. 
Although  the  following  answers  have  been  checked  by  at  least  two 
teachers,  of  course  some  mistakes  have  crept  in,  and  the  author  will 
appreciate  it  if  anyone  finding  such  errors  will  notify  him. 

The  results  were  read  from  a slide  rule  and  may  vary  by  1 in  the 
last  place. 

Thanks  are  due  to  Mr.  F.  A.  Clark,  Pratt  Institute,  to  Mr.  F.  R. 
Lufkin,  Franklin  Union,  and  to  Mr.  C.  W.  Bates,  Yale  University, 
^ for  their  competent  work  in  checking  the  results. 


Boston,  Mass 


W.  EL  Timbie. 
iii 


V* 


I 


ANSWERS  TO  PROBLEMS 


CHAPTER  I 

1.  3,000,000  lines. 

2.  1250  sq.cms. 

3.  5000  gausses. 

4.  21,600  gausses. 

5.  6.67  gausses. 

6.  668  unit  poles. 

7.  2.52  lbs. 

8.  3.67  cms. 

9.  11.7  unit  poles. 

10.  222.5  gausses. 

11.  55.6  and  88.9  respectively. 

12.  .1  lb. 

16.  285  unit  poles. 

18.  (a)  6400  unit  poles. 

(b)  80,500  lines. 

19.  .23  lb.  or  102,400  dynes. 

20.  3000  gausses. 

21.  80  dynes. 

23.  (a)  .0126  1b. 

(b)  20  gausses;  11.2  gausses. 

24.  (a)  .108  lb. 

(b)  1.58  cms. 

(c)  .108  1b. 

25.  .644  lb. 

26.  .322  1b. 

27.  6280  lines. 

28.  31.3  gausses. 

29.  25,000  gausses. 

30.  11,900  unit  poles. 

31.  .837  1b. 

32.  1600. 

33.  12.6  cms. 

34.  56,800  gausses. 


35.  (a)  31.3  gausses. 

(b)  8.94  cms. 

36.  13,000,000  lines. 

CHAPTER  II 

1.  .264  volt. 

2.  4800  ft. 

3.  .962  ohm. 

4.  220  ohms. 

5.  20  amps. 

6.  2 amps. 

7.  5 ohms. 

8.  16  volts. 

9.  30  volts. 

10.  11  ohms. 

11.  40  amps. 

12.  25  amps. 

13.  12  volts. 

14.  4 volts. 

15.  57.5  ohms. 

16.  (a)  .08  amps. 

(b)  10  volts. 

17.  (a)  204  volts. 

( b ) 203  volts. 

18.  (a)  1.15  amp, 

(b)  115  volts. 

(c)  4.60  volts. 

19.  (1)  32  volts. 

(2)  12  volts. 

(3)  32  volts. 

(4)  972  volts. 

20.  (a)  .5  amp. 

(b)  .450  ohms. 

j 21.  1.5  amp. 


VI 


ANSWERS  TO  PROBLEMS 


22.  5 mhos;  .2  ohm. 

23.  2 and  6 amps,  respectively. 

24.  17.4  volts. 

25.  110  ohms. 

26.  100  volts. 

27.  15,760  volts. 

28.  20  amps. 

29.  A B and  DE  2 amps. 

BC  and  EF  .8  amp. 

30.  52  volts. 

31.  2.05  mhos;  .488  ohm. 

32.  A to  B 12  amps. 

B to  F 8 amps. 

B to  C 4 amps. 

C to  E 12  amps. 

33.  .8  amp;  12  volts. 

34.  (a)  16  volts. 

( b ) 204  volts. 

(c)  102  ohms. 

35.  .002  milamp. 

36.  93.2;  69.8;  37.2  volts  respect- 

ively. 

4.66  amps. 

37.  560  volts. 

38.  120  volts. 

39.  1 volt. 

40.  .016  ohm. 

41.  3.66  ohms. 

42.  (a)  66  volts. 

(5)  4.8  volts. 

(c)  70.8  volts. 

43.  (a)  Across  CD,  117.5  volts. 

“ EF,  113  volts. 

(b)  235  ohms. 

(c)  226  ohms. 

(d)  12  volts. 

44.  (a)  110  volts. 

(6)  1.67  ohms. 

45.  2.18  volts. 

46.  (a)  Between  A and  B. 

( b ) Across  A,  99  volts. 

“ B,  87  “ 

(c)  8 volts. 


47.  (a)  .734  and  1.10  amps,  re- 

pectively. 

(b)  .734  and  55  amps,  re- 

spectively. 

(c)  60  and  1.97  ohms  respect- 

ively. 

48.  (a)  Through  A .281  amp. 

“ B .234  amp. 

“ C .512  amp. 

(b)  54.5  ohms. 

(c)  214.5  ohms. 

( d ) Across  A and  B,  28.1  volts. 
Across  C,  81.9  volts. 

49.  Current  through  y,  7.5  amps. 

“ “ z,  10  amps. 

Resistance  of  x,  15  ohms. 
Voltage  B to  C,  37.5  volts. 

50.  1596  volts. 

1584  volts. 

51.  (a)  Across  Li,  110  volts. 

“ M2,  114  volts. 

(6)  .200  ohm. 

52.  (a)  2.5  amps. 

(5)  10  volts. 

(c)  120  volts. 

(1 d ) 132.5  volts. 

( e ) 12.5  volts. 

53.  (a)  112.4  volts. 

( b ) 75  ohms. 

(c)  4 volts. 

(d)  3.6  volts. 

(e)  Through  each  lamp  of 

A,  1.16  amps. 

Through  each  lamp  of 

B,  1.50  amps. 

54.  (a)  113.9  volts. 

(6)  104.5  ohms. 

(c)  4 volts. 

(d)  2.09  volts. 

(e)  Through  each  lamp  of 

A,  1.16  amps. 

Through  each  lamp  of 

B,  1.087  amps. 


ANSWERS  TO  PROBLEMS 


vil 


55.  194.5  volts. 

56.  (a)  Across  car  I,  511.8  volts. 

“ II,  471.3  volts. 
“ III,  460  volts. 

( b ) 90  volts. 

57.  (a)  Across  car  I,  533.8  volts. 

“ II,  516.6  volts. 
lt  III,  511.8  volts. 
(b)  38.2  volts. 

CHAPTER  IV 

1.  2.43  H.P. 

2.  1.81  K.W. 

3.  55  watts. 

4.  3.03  K.W. 

5.  265  watts. 

6.  32  watts. 

7.  660  watts. 

8.  2.20  K.W. 

.180  K.W. 

9.  135  watts. 

10.  62.6  H.P. 

11.  $1.76. 

12.  $1.89. 

13.  .200  K.W.  hour. 

14.  $0.19. 

15.  96  K.W.  hrs. 

16.  1.37  K.W. 

17.  .455  amp. 

18.  $0.91. 

19.  2.55  K.W.  hrs. 

20.  5,200,000  ft.-lbs.  less. 

21.  332,000  cals. 

22.  .0000139  cents. 

23.  2,850,000  cals. 

24.  45,700  cals. 

25.  293,000  cals. 

26.  1.68  hrs. 

27.  78.4%. 

28.  61  amps. 

29.  77.5%. 

30.  95%. 

31.  93.3%. 


32.  92.7%. 

33.  91.7%. 

34.  92.8%. 

35.  91.9%. 

36.  91.7%. 

37..94.6%. 

38.  3.44  watts  per  c.p. 

39.  33.3  c.p. 

40.  (a)  87.3%. 

(6)  12-7%. 

(c)  3.19  watts  per  c.p. 

41.  (a)  .045  ohm. 

(6)  .0009  ohm. 

(c)  .003  ohm. 

{d)  36,700  amps. 

42.  .00734  amp. 

43.  (a)  170  volts. 

(b)  64.7%. 

44.  92.3%. 

45.  9.9  K.W. 

13.3  H.P. 

46.  60.5  watts. 

47.  162  watts. 

48.  88.5%. 

49.  90.5  amps. 

50.  109  amps. 

51.  $0.67. 

52.  $43.90. 

53.  (a)  250  ohms. 

(b)  62.5  watts;  .0838  H.P. 

54.  14.7°  C.  per  min. 

55.  3.4  mins. 

56.  (a)  Across  A,  117  volts. 

“ B,  114.6  volts. 

(i b ) In  CD  and  GM,  3 volts. 
In  DE  and  FG,  2.4  volts. 

(c)  A takes  234  watts. 

B takes  343.8  watts. 

(i d ) 22.2  watts. 

(e)  96.3%. 

57.  (a)  125  watts. 

(b)  77.3%. 

.688  watts  per  c.p. 


Vlll 


ANSWERS  TO  PROBLEMS 


58.  $159.00. 

59.  50.8  H.P. 

60.  (1)  2.5  ohms. 

(2)  10.96  volts, 

(3)  126  volts 

(4)  148  volts 

(5)  89.9%. 

(6)  166  ohms. 

(7)  220  ohms. 

61.  (a)  200  watts. 

(b)  589  volts;  8.15  amps, 
(e)  613  volts. 

62.  $1.50  gain. 

63.  (a)  2.83  ohms. 

(6)  389  watts. 

(c)  (, S ) 2.79  watts. 

(R)  142  watts. 

(d)  (1)  62.8%. 

(2)  .65  watts  per  c.p. 

64.  208°  C. 

CHAPTER  V 

1.  26,900  C.M. 

2.  4,760,000  C.M. 

3.  3910  C.M. 

4.  .707  in. 

5.  (a)  .00307  sq.in. 

(b)  3070  sq.  mils. 

6.  .667  ohm. 

7.  3150  ft. 

8.  .234  in. 

9.  2.04  in. 

10.  .506  amp. 

11.  416  volts. 

12.  14  ohms. 

13.  .314  in. 

14.  28.3  sq.in. 

15.  5.32  ohms. 

16.  262  ohms. 

17.  186  ohms. 

18.  206  ohms. 

19.  38.1°  C. 

20.  211  ohms. 


21.  1.82  ohms. 

22.  45°  C. 

23.  210°  C.;  .0043  coeff. 

24.  About  No.  3. 

25.  No.  0. 

26.  .508  in. 

27.  450  ohms. 

28.  426  ohms. 

29.  10,000  ohms. 

30.  8.33  ohms. 

31.  BA,  15.1  cms. 

DA,  84.9  cms. 

32.  3700  ft. 

33.  2220  ft. 

34.  3290ft. 

35.  1300  ft. 

36.  218  ft. 

37.  (a)  58.9. 

(b)  1.30  megs. 

38.  5.41  volts. 

39.  169  volts. 

40.  15.0  volts;  272  watts. 

41.  .483  in. 

42.  No.  7 (B.  & S.). 

43.  5071  ft. 

44.  .152  in. 

45.  342,000  C.M. 

46.  .564  in. 

47.  167  amps. 

48.  .463  ohms. 

49.  21.3  volts. 

50.  2890  volts. 

51.  3470  volts  E.M.F. 

2820  volts  Brush  Pot. 

52.  77.8%  and  79.8%. 

53.  .00137  milamp. 

54.  5.04  megs. 

55.  278,000  C.M. 

56.  (1)  AB,  340  watts. 

CD,  27.6  watts;  FG,  54.2 
watts. 

BC,  70.7  watts;  EF,  22.7 
watts. 


ANSWERS  TO  PROBLEMS 


IX 


56.  GH,  17.7  watts. 

(2)  (I)  102.7  volts;  (II)  101.5 
volts;  (III)  103.8  volts. 

(3)  82.4%. 

57.  2.43  ohms. 

58.  Yes.  40°  C rise. 

59.  1.71  amps. 

60.  40.6  ft.  (hard);  43.2  ft. 

(soft). 

61.  No.  2. 

581  volts. 

1.56  K.W.,  94.7%. 

62.  No.  00,  567  volts;  780  watts, 

97.2  %. 

63.  119.2  volts;  92.2%. 

64.  428,000  C.M. 

65.  380,000  C.M. 

66.  266,000  C.M. 

67.  In  AB,  .05  amp. 

AD,  .25  amp. 

BD,  0. 

BC,  .05  amp. 

DC,  .25  amp. 

68.  1,630,000  C.M. 

69.  405,000  ohms. 

CHAPTER  VI 

1.  10.08  gausses. 

2.  5040  gausses. 

3.  12.7  amp.  turns  per  cm. 

4.  509  amp.  turns. 

5.  (a)  9 gausses 

(b)  7.16  amp.  turns  per  cm. 

6.  .143  amp. 

7.  71.5  amp.  turns. 

8.  18,900  gausses. 

9.  317  amp.  turns. 

10.  18,000  gausses. 

11.  (a)  27,000  lines. 

(b)  2150  unit  poles. 

12.  .922  amp. 

13.  40,000  units. 


14.  31,800  amp.  turns. 

15.  .00396  units. 

16.  6.5  amps. 

17.  .0188  unit. 

18.  .0291  unit. 

19.  1.20988  units. 

20.  597  amp.  turns. 

21.  12,470  amp.  turns. 

22.  2.57  amps. 

23.  555  amp.  turns. 

24.  242  turns. 

25.  48,000  gausses. 

26.  41,100  amp.  turns. 

27.  101,200  amp.  turns. 

28.  1.62  amp.  (4000  turns). 

29.  .145  K.W. 

30.  (a)  133  sq.cms. 

(5)  1720. 

(c)  557  amp.  turns. 

(< d ) .000875. 

31.  108  volts. 

32.  2650  ft. 

33.  45.1  volts. 

34.  33.5  amp.  turns. 

35.  14,900  amp.  turns. 

36.  3.15  amps. 

37.  .456  amp. 

38.  13,500  amp.  turns. 

39.  1st,  100  sq.cms.;  2nd,  71.4 

sq.cms.;  3rd,  133  sq.cms.; 
4th,  83.4  sq.cms. 

40.  .0171  unit. 

41.  34,500  amp.  turns. 

42.  .094  unit;  46.3. 

43.  .0198  unit;  221. 

44.  4670  amp.  turns. 

45.  59,000  amp.  turns. 

46.  .55  K.W. 

47.  248  K.W. 

48.  7600  amp.  turns  for  the  two 

coils. 

49.  2.475  amps. 

50.  27.1  watts. 


X 


ANSWERS  TO  PROBLEMS 


51.  3.5  inches. 

52.  4.13  inches. 

53.  51°  C. 

CHAPTER  VII 

1.  125  volts. 

2.  .8  volt. 

3.  9.6  volts. 

4.  150  ft.  per  sec. 

5.  (a)  .198  ohm. 

( b ) .0331  ohm. 

(c)  .0055  ohm. 

6.  .00614  ohm. 

7.  3620  ft. 

8.  .0081  ohm. 

9.  129.73  volts. 

10.  960  volts. 

11.  98.8  volts. 

12.  96.34  volts. 

13.  2300  volts. 

14.  12.1%.  v 

15.  75  amps. 

16.  126.17  volts. 

17.  66.2  amps. 

18.  12  turns. 

19.  66.7  volts. 

20.  223  watts. 

21.  37.1  watts. 

22.  (a)  6.17  watts. 

(6)  55.6  volts. 

23.  .0497  H.P. 

24.  334  volts. 

25.  .349  ohm. 

26.  121.5  amps, 

27.  291.6  volts. 

28.  (a)  35.5  K.W. 

(b)  14.5%. 

29.  1.296  K.W. 

30.  640  volts. 

31.  267  R.P.M. 

32.  1080  volts. 

33.  211  K.W. 

34.  2.27%. 

35.  640  volts. 


36.  .155  ohm. 

37.  334  volts. 

38.  (a)  0.5  amp. 

(6)  55  watts. 

39.  (a)  2000  turns. 

(6)  110  turns. 

40.  670  volts. 

41.  27,900,000  lines. 

42.  1,550,000  lines. 

43.  149.4  volts. 

44.  (a)  554  volts. 

( b ) 61  amp^. 

45.  .33  ohm. 

46.  25.9  amps. 

47.  118.5  volts. 

48.  511,000  lines. 

49.  .0206  ohm;  103.7  amps. 

50.  1033  gausses. 

51.  1062  gausses. 

52.  116.8  volts. 

53.  21  amps. 

54.  1379  volts. 

55.  (a)  1429  volts. 

(5)  1424  volts. 

56.  504  conductors. 

57.  (1)  120.4  volts. 

(2)  106.34  amps. 

58.  120.3  volts;  106.45  amps. 

59.  .662  ohm. 

60.  6 poles. 

61.  2,670,000  lines. 

62.  (a)  343.5  amps. 

(b)  3.51  amps.;  340  amps. 

(c)  127.4  volts. 

63.  120.2  volts;  40.9  K.W. 

64.  Arm.  current,  343.4  amps. 
Series  field  current,  343.4 

amps. 

Shunt  field,  3.44  amps. 
E.M.F.,  127.4. 

Terminal  volt,  120.2. 

40.9  K.W. 

65.  6320  amp.  turns. 


ANSWERS  TO  PROBLEMS 


xi 


CHAPTER  VIII 

1.  12,450  gausses. 

2.  15.9  amps. 

3.  ( b ) Counterclockwise, 
(c)  3.60  lbs. 

4.  4.50  lb.  ft. 

5.  9.00  lb.  ft. 

6.  .304  lb.  ft. 

9 7.  Clockwise. 

8.  .5  ohm. 

9.  108.8  volts. 

10.  288  amps. 

11.  560  amps. 

12.  (a)  7.67  amps. 

(b)  .523  amp. 

13.  (a)  9.00  amps. 

( b ) .512  amp. 

14.  (a)  10.8  amps. 

( b ) .503  amp. 

15.  (a)  13.3  amps. 

(b)  .496  amp. 

16.  (a)  4.00  amps. 

(6)  .494  amp. 

17.  112.6  volts. 

18.  .5  ohm. 

19.  No  turning  tendency. 

20.  3.2  lbs. 

21.  2.66  lb.  ft. 

22.  (a)  208  volts. 

( b ) 2.50  K.W. 

* 23.  230  lbs. 

24.  1.07  lbs. 

25.  (a)  514  lbs. 

p (6)  321  lb.  ft. 

26.  (a)  66.1  H.P. 

( b ) 936  volts. 

27.  891  volts. 

28.  (a)  3.00  ohms 
(6)  .75  ohm. 

29.  8.1% 

30.  (a)  55  amps. 

( b ) .55  amp. 


31.  (a)  1 amp. 

(6)  .55  amp. 

32.  (a)  9.94  amps. 

(b)  3.70  amps. 

33.  100  volts. 

34.  (a)  Field  1.92  amps. 

Arm.  78.1  amps. 

(5)  .466  K.W. 

35.  (a)  .500  amp. 

(5)  .496. 

36.  (a)  9.2  K.W. 

(c)  111.9  volts. 

37.  (a)  92.7  volts. 

(b)  Field,  122  watts. 

Arm.,  307  watts. 

38.  (a)  72.2  volts. 

(b)  1.227  K.W. 

39.  (a)  Arm.,  139.6  amps. 

Field,  3.15  amps. 

(b)  118.4  volts. 

40.  772  R.P.M. 

41.  1520  R.P.M. 

42.  1520  R.P.M. 

43.  760  R.P.M. 

44.  7.45%. 

45.  4.44%. 

46.  .506  ohm. 

47.  7,500,000  lines. 

48.  1390  R.P.M. 

49.  (a)  102.4  volts. 

(b)  118.4  volts. 

50.  42  lb.  ft. 

CHAPTER  IX 

3.  (a)  1 K.W. 

( b ) .16  K.W. 

4.  110  volt  line  has  four  times 

as  heavy  wire. 

5.  No.  5 B.  & S. 

6.  744  volts. 

7.  761  volts. 

8.  (a)  AR  = 24amps. 


ANSWERS  TO  PROBLEMS 


xii 


8.  DF  = 32amps. 

CD  = 8 amps. 

( b ) AB  = 7.2  volts. 

EF  = 9.6  volts. 

CD  = 2.4  volts. 

(c)  499  watts. 

(d)  BD  = 105.2  volts. 

DE  = 98  volts. 

(e)  92%. 

(/)  DD,  4.38  ohms. 

DE , 3.06  ohms. 

9.  Across  DD,  120  volts. 

“ DE,  83.7  volts. 

10.  Across  I,  118.72  volts. 

“ II,  120.51  volts. 

11.  98.4%. 

12.  Through  Ei,  3.185  amps. 

“ E2,  1.455  amps. 

1 1 line,  4.64  amps. 

13.  (a)  6.67  amps. 

(b)  3.34  volts. 

14.  (a)  line,  11.65  amps. 

16.1  amps. 

4.45  amps. 

(b)  116.5  volts. 

15.  516.4  watts. 

10.  960  watts. 

17.  523  watts. 

18.  87.7%;  94%. 

19.  88.2%;  93.4%. 

20.  95.5%. 

21.  96.5%;  93.8%. 

22.  (a)  88.4%. 

(b)  93.1%. 

23.  95.2%;  85.8%. 

21.  775  watts. 

25.  (a)  9130  watts. 

(b)  94.8%. 

20.  Curve. 

27.  11,000  volts,  No.  9 B.  & S. 

28.  Curve. 

29.  At  30,000  volts,  21,200  C.M. 

30.  1,180,000  C.M. 


31.  (a)  118.8  volts. 

(5)  96.8%. 

(c)  95.7%. 

32.  100  amp.  car,  422  volts. 

60  amp.  car,  470  volts. 

33.  2 cars,  nearest  gen.,  439  volts. 
2 cars,  furthest  from  gen.,  414 

volts. 

34.  100  amp.  car,  352  volts. 

60  amp.  car,  401  volts. 

35.  (a)  Car  I,  536  volts. 

Car  II,  485.8  volts. 

Car  III,  464.1  volts. 

(b)  87.4%. 

36.  Car  T 534  volts. 

Car  II,  481.3  volts. 

Car  III,  459.6  volts. 

37.  8.3  volts. 

38.  (a)  87.3%;  93.0%. 

(b)  86.4%. 

(c)  75.3%. 

39.  (a)  27.4  amps. 

(5)  106.3  volts. 

(c)  2.555  volts. 

40.  23.62  amps. 

41.  11.95  amps. 

42.  (a)  117.95  volts. 

(b)  119.4  volts. 

43.  23.17  amps. 

44.  11.8  amps. 

45.  .948  ohm. 

46.  6 parallel  rows  of  53  cells  in 

series. 

47.  Input,  7.5  K.W. 

Output,  8.53  H.P. 

Efficiency,  84.7%. 

48.  (a)  MR,  2.8  volts. 

RT,  1.2  volts. 

OS,  .8  volt. 

SV,  .8  volt. 

NW,  4 volts. 

(6)  Across  A,  106.4  volts. 

1 1 B,  106  volts. 


ANSWERS  TO  PROBLEMS 


48.  Across  C , 106  volts. 

(c)  ft,  1.54  K.W. 
ft,  1.10  K.W. 

(d)  96.5%. 

49.  (a)  MR,  2.33  volts. 

i£T,  1.00  volt. 

SV,  1.32  volts. 

ATT,  4.65  volts. 

(6)  Across  A,  88.4  volts. 
“ B,  88.7  volts. 
“ C,  123.3  volts. 

(c)  <?!+&  = 2.56  K.W. 

(d)  96.3%. 

50.  (a)  Afft  3.07  volts. 

AT7,  1.51  volts. 

OS,  1.59  volts. 

NW,  3.01  volts. 

(5)  Across  A,  105.3  volts. 
“ B,  133  volts. 

“ C,  79.7  volts. 

(c)  ft,  1.70  K.W. 
ft,  .828  K.W. 

(d)  96.3%. 

51.  (a)  A,  91.7  volts. 

ft  91.5  volts, 
ft  72.1  volts, 
ft  110.4  volts. 

52.  (a)  A,  100.3  volts. 

B,  99  volts, 
ft  77.6  volts, 
ft  117.6  volts. 

53.  (a)  A,  78.5  volts. 

63.6  volts, 
ft  19.6  volts, 
ft  115.6  volts. 

54.  1.193  amps.;  2.39  volts. 

55.  (a)  1.17  amps. 

( b ) 2.33  volts. 

56.  (a)  5.31  H.P. 

( b ) 88.3%;  95.2%. 

57.  (a)  I,  127.1  volts. 

II,  128  volts. 

(h)  ft,  129.4  volts. 


57.  ft,  133.5  volts. 

58.  96.5%. 

59.  ft,  92.4%. 
ft,  95.6%. 

60.  753  watts. 

61.  94.2%;  84.6%. 

62.  94.2%;  84.6%. 

63.  83.2%;  88.3%. 

64.  83.2%;  88.3%. 

05.  R,  .0936  amp. 

Ri,  .144  amp. 

R2,  .110  amp. 

Rz,  .128  amp. 

Gal.,  .0164  amp. 

66.  6,500,000  C.M. 

67.  11,140,000  C.M. 

68.  3,200,000  C.M. 

CHAPTER  X 

1.  4.11  henrys. 

2.  197  volts. 

3.  .00843  henry. 

4.  Prim.,  .705  henry. 
Sec.,  70.5  henrys. 

5.  3.02  henrys. 

6.  .00021  henry. 

7.  .336  henry. 

8.  (a)  .021  volt. 

(6)  33.6  volts. 

9.  33.6  volts. 

10.  .371  henry. 

11.  740  volts. 

12.  .400  henry. 

13.  32  volts. 

14.  550  times. 

15.  (a)  .00180  henry, 

(6)  3.60  henrys. 

16.  121  henrys. 

17.  1.21  henrys. 

18.  .0689  amp. 

19.  200  volts. 

20.  1466  turns. 


XIV 


ANSWERS  TO  PROBLEMS 


21.  1430. 

22.  4.8  henry s. 

23.  31.7  henry s. 

24.  Prim.,  317  henrys. 
Sec.,  3.17  henrys. 

25.  .035  amp. 

26.  110  volts. 

27.  .734  henry. 

28.  384  henrys. 

29.  188  turns. 

30.  4320  volts. 


CHAPTER  XI 

1.  10.9  mfs. 

2.  642  volts. 

3.  .0044  coulomb. 

4.  .0275  amp. 

5.  .055  amp. 

6.  1510  watts. 

7.  .484  watt-secs. 

8*  .00032  secs. 

9.  6.88  amp;  755  watts;  .484 
watt-secs. 

19.  20  amps.;  6420  watts:  2.25 
watt-secs. 

11.  .00035  secs. 

12. , (a)  .121  watt-sec. 

(6)  .484  watt-sec. 

13.  1.59  mfs. 

14.  .000319  coulcomb. 

15.  .465  mf.  (K  = 2.5). 

16.  8.05  mfs.  (K  = 2.5). 

17.  .0084  mf. 

18.  .179  mf. 

19.  .534  mf. 

22.  1170  ft. 

23.  1.32  mfs. 

24.  .00066  coulomb. 

25.  (a)  .00044  coulomb. 

( b ) .0011  coulomb. 

26.  .000157  coulomb. 

27.  Ei  = 30  volts. 


27.  E2  = 80  volts. 

28.  2.79  mfs.  (K=  2.1). 

29.  7.98  mfs. 

30.  10.77  mfs. 

31.  2.07  mfs. 

32.  .00119  coulomb. 

33.  .00414  amp. 

34.  2600  ft. 

35.  4 in  series  with  1 and  3 in 

parallel. 

2 mfs. 

35.  0.0254  watt-sec. 

37.  .000042  sec. 

38.  .000277  sec. 

39.  .000035  sec. 

49.  176  volts. 

41.  330  volts. 

42.  10  mfs.  has  .00176  coulomb. 
15  mfs.  “ .00264 

43.  .00198  coulomb. 


CHAPTER  XII 

1.  148  gms. 

2.  46.7  hrs. 

3.  19.2  amps. 

4.  255  hrs. 

5.  71.9  hrs.  and  77.9  hrs. 

6.  1.17  amp. 

7.  1.15%  high. 

8.  .914  oz. 

9.  (a)  27.3  amps. 

( b ) 219  amp.  hrs. 

10.  (a)  1.54  sq.ft. 

( b ) 80  amp.  hrs. 

11.  2.31  sq.ft. 

12.  .0267. 

13.  2.64  volts. 

14.  .16  volt. 

15.  Charge,  2.32  volts. 
Discharge,  2.08  volts. 

16.  .325  ohm. 

17  7 end  cells. 


ANSWERS  TO  PROBLEMS 


xy 


18.  56  cells. 

19.  .988  ohm. 

20.  6 cells. 

21.  1.5  mi. 

22.  More  than  13.3  amps. 

23.  153  hrs. 

24.  65.6  hrs. 

25.  .000138  in. 

26.  Zinc,  $0,134  per  K.W.  hr. 
Coal,  $0,010  per  K.W.hr. 

27.  4.97  ohms. 

28.  3.36  ohms. 

29.  91.28  volts. 

30.  169.4  volts. 

31.  92.37  volts. 

32.  4.81  ohms. 

33.  .77  ohm. 

34.  1368  R.P.M. 

35.  (a)  104  amp.  hrs. 

(6)  4.44  K.W.  hrs. 

36.  (a)  218  amp.  hrs. 

(b)  36.8  K.W.  hrs. 

37.  2 parallel  sets  of  45  in  series. 

38.  (a)  6 parallel  sets  of  15  in  series. 
( b ) 31.8  volts. 

39.  .0075  ohm. 

40.  103.5  amps. 

41.  479  volts. 

42.  82.2  amps. 

43.  314  amps. 

44.  Delivering  11  amps. 

45.  (a)  189.3  amps. 

(b)  Receiving  39.3  amps. 

CHAPTER  XIII 

1.  (a)  1.28  ft.  candles. 

(b)  3.54  ft. 

2.  (a)  2.82  ft. 

2.  (b)  4 ft. 

3.  7.55  ft. 

4.  3.9  X1016  c.p. 

6.  18.9  c.p. 


7.  A=4x. 

8.  15.6  c.p. 

9.  3.8  watts  per  c.p. 

10.  67%  longer. 

11.  52%  of  normal  life;  18.5  c.p. 
2.92  watts  per  c.p. 

12.  27.8  c.p. 

13.  1.03  ft.  candle. 

14.  980  c.p. 

15.  .05  ft.  candle. 

16.  150  cms. 

16a.  AE  = 29.8  c.p. 

BF  — 27.8  c.p. 

17.  11.3  c.p. 

18.  .5  ft.  candle. 

19.  .36  ft.  candle. 

20.  .311  ft.  candle. 

21.  .306  ft.  candle. 

22.  (1)  .526  ft.  candle. 

(2)  .142  ft.  candle. 

(3)  .306  ft.  candle. 

(4)  .320  ft.  candle. 

23.  (5)  .202  ft.  candle. 

(6)  .106  ft.  candle. 

(7)  .152  ft.  candle. 

(6)  .504  ft.  candle. 


CHAPTER  XIV 

1.  1-11. 

2.  111.1  ohms. 

3.  562  divisions. 

4.  51.1  ohms. 

5.  .0101  ohms. 

6.  .484  amp.  or  8.8%  low0 

7.  .185  amp.  low. 

8.  1.928  amps.  low. 

9.  14,995  ohms. 

10.  .000333  ohm. 

11.  20,000  ohms. 

12.  5.1  volts  low. 

13.  .2  volt  low. 


XVI 


ANSWERS  TO  PROBLEMS 


14.  (a)  3.75°. 

(b)  60°. 

(c)  113.5°. 

15.  (a)  1.63  amps. 

( b ) 3.27  amps. 

(c)  4.47  amps. 

16.  1.48%  high. 

17.  (a)  .458  amp.;  112  volts. 

(b)  .04  of  1%  high. 

18.  60.5  watts. 

19.  60.5  watts;  110  volts;  .634 

amp. 

20.  1.4283  volts. 

21.  28.566. 

CHAPTER  XV 

1.  1090  volts. 

2.  —410  volts. 

3.  414  volts. 

4.  308  volts. 

6.  20°  = 205  volts. 

80°  = 591  volts. 

130°  = 460  volts. 

210°  = —300  volts. 

300°  = —520  volts. 

340°  = —205  volts. 

7.  12,580  volts. 

8.  10,900  volts. 

9.  38,400  volts. 

10.  60,400  volts. 

11.  42,700  volts.  No. 

12.  15.4  amps. 

13.  15.4  amps. 

14.  180°  =0  amp. 

200°  = — 5.27  amps. 

300°  = — 13.3  amps. 

15.  35.4  amps. 

16.  22.5  amps. 

17.  142  amps. 

18.  707  volts. 

19.  8880  volts. 

20.  42,700  volts. 

21.  6.25  amps. 


22.  6.94  amps. 

23.  6.00  amps. 

24.  37.5°. 

25.  —34.2  amps. 

26.  (a)  320  volts. 

(b)  355  volts. 

(c)  503  volts. 

27.  (a)  22.5°;  (b)  192  volts. 

28.  141  volts;  45  amps. 

29.  (a)  38.8  amps. 

(b)  27.5  amps. 

30.  (a)  779  volts. 

(b)  495  volts. 

31.  14°  lag. 

32.  108  amps. 

33.  —32.2  amps. 

34.  68.4  volts. 

35.  (a)  27.8  amps. 

(b)  726  volts. 

36.  12.35  ohms. 

37.  111°. 

38.  113  volts. 

39.  0. 

40.  62.7  amps. 

41.  41  amps.,  44  volts. 

42.  55  ohms. 

43.  1.8  amps. 

44.  707  volts. 

45.  (a)  —968  volts. 

(b)  284.4°. 

46.  3.65  amps. 

47.  29°  current;  119°  voltage; 

136  volts. 

48.  29.2  cycles  per  sec. 

49.  36.7  ohms. 

50.  .0165  henry. 

51.  43.4  amps. 

52.  .73  amp. 

53.  7.25  amps. 

54.  —488  volts. 

55.  162  volts. 

56.  .738  amp. 

57.  17.1  amps.  (K  = 1.S6). 


ANSWERS  TO  PROBLEMS 


xvn 


i 


y 


B 


* 


* 


58.  17.6  amps. 

59.  3280  ohms. 

60.  .168  amp. 

61.  .34  amp. 

62.  1.34  amps. 

63.  —.416  amp. 

64.  .953  amp. 

65.  60.2  ohms. 

66.  9.14  amps. 

67.  37  ohms. 

68.  4.19  amps. 

69.  96.3  ohms. 

70.  1.14  amps. 

71.  8.59  amps. 

72.  Across  reactance,  171.8  volts. 

11  R,  137.4  volts. 

73.  Current  leads  voltage  51.3°. 

74.  (a)  20.5  amps. 

(6)  (1)  287  volts. 

(2)  410  volts. 

(3)  246  volts. 

(4)  205  volts. 

(5)  82  volts. 

(c)  Current  leads  26.6°. 

75.  (a)  Across  XL  =32  volts. 

“ Ac  = 8 volts. 

(6)  Across  combin.  = 31.2 
volts. 

(c)  Current  lags  50°  20'. 

76.  41.8  amps. 

77.  Current  lags  62.9°. 

78.  .523  amp. 

79.  Current  leads  41°. 

80.  1.04  amps. 

81.  2.22  amps.;  current  lags  57.5°. 

82.  Through  AB,  1.29  amps. 

‘ 1 CD,  3.45  amps. 

11  FG,  3.69  amps. 

Current  in  FG  lags  10  min. 

83.  1.358  K.W. 

U.  .98. 

85.  2.32  K.W. 

86,  2.14  amps. 


87.  (a)  11  amps. 

(6)  1.21  K.W. 

88.  1.45  amps. 

89.  21  watts. 

90.  (a)  65%. 

(6)  2.55  K.W. 

91.  90.9%;  24.7°. 

92.  87  volts. 

93.  15.5  amps. 

94.  17.2  amps. 

95.  (a)  5°  lag. 

(6)  99.6%. 

(c)  1.22  K.W. 

0 d ) 1.63  K.W. 

96.  (a)  143  volts. 

( b ) 107.5  volts. 

(c)  — 132  volts. 

97.  i = 189  sin  cj>. 

98.  (a)  108  amperes. 

(b)  —90.6  amperes. 

99.  (a)  161  volts. 

(b)  279  volts. 

(c)  96  volts. 

100.  (a)  420  volts. 

(b)  —34.2  volts. 

(c)  431  volts. 

101.  (a)  59.5  amps. 

(6)  11.1°  lag. 

102.  (a)  4.53  K.W. 

(6)  2.02  K.W. 

(c)  6.55  K.W. 

103.  / branch,  6.03  K.W. 

7,  “ 1.40  K.W. 

104.  200  volts. 

105.  (a)  5000  watts. 

( b ) 25  amps. 

106.  200  volts. 

107.  i — 35.3  sin  e = 282  sin 

e = 282  sin  i = 35.3  sin 
(4>  — 90°). 

108.  (a)  200  volts. 

( b ) e — 282  sin  4> ; i = 35.3  sin 
(£+90°). 


xviii  ANSWERS  TO  PROBLEMS 


109.  1.46  amps. 

110.  (a)  1.43  amps. 

(i b ) 78.8°. 

111.  (a)  e = 156  sin  4>;  i = 2.02 

sin  ($  — 78.8°). 

(6)  30.7  watts. 

112.  e = 156  sin  <j>;  ?=2.07  sin 

(cf> — 90°). 

None. 

113.  3.16  amps. 

64.5°. 

e = 156  sin  <j>;  i = 4.47  sin 
(([>— 64.5°). 

150  watts. 

114.  7.33  amps. 

805  watts. 

115.  —1.98  amps. 

116.  e =640  sin  ($+51.4°). 

117.  (a)  500  volts. 

(b)  1000  watts. 

118.  594  volts  across  combination. 
589  volts  across  X. 

75  volts  across  R. 

119.  196  amps. 

197.6  amps. 

129.  68.8  volts. 

121.  .182  amps. 

122.  881  volts. 

123.  98.3  K.W. 

124.  .999985;  98.3% 

125.  R = 4.89  ohms. 


Xz/  = 3.03  ohms. 

Z =5.75  ohms. 

126.  (a)  58.5  volts. 

( b ) 147  volts. 

(c)  51.7  volts. 

(d)  4.89  amps. 

127.  (a)  .523. 

(5)  By  R = 286  watts. 
Xl  — 0 watts. 

Xc  — 0 watts. 

128.  (a)  2.3  amps. 

(5)  77.3  volts;  32.2. 

(c)  4.7°  lag. 

129.  (a)  3.28  amps.;  7.9  amps. 

(6)  110  volts. 

(c)  In  pi  ase. 

130.  143  volts. 

131.  (a)  32.86  volts. 

(5)  77.5%. 

132.  862  watts. 

133.  489  mfs. 

134.  10.9  ohms. 

135.  113  amps. 

136.  96%. 

137.  56.4  amps. 

138.  28.2  amps. 

139.  (a)  500  amps. 

( b ) 866  amps. 

(c)  500  amps. 

140.  173  volts. 


J 

i 


5 


J 

■* 


■v 


0 


10 


i 


v 


i 


r 


*} 


